Enhanced Privacy ID (EPID) grew from the work of Ernie Brickell and Jiangtao Li based on previous work on Direct Anonymous Attestations (DAA). DAA is very relevant because it is built-in into the TPM1.2 chip (of which there are several hundred million in PC machines).

Here is a quick summary of EPID:

EPID is a special digital signature scheme.

One public key corresponds to multiple private keys.

Private key generates a EPID signature.

EPID signature can be verified using the public key.

Interesting Security Properties:

Anonymous/Unlinkable: Given two EPID signatures one cannot determine whether they are generated from one or two private keys.

Unforgeable: Without a private key one cannot create a valid signature.